Abstract:The structure of feedforward inverses is a fundamental problem in the invertibility theory of finite automata. The characterization of the structure of feedforward inverses with delay steps ≥3 is a long-term unsolved problem. This paper deals with this topic. For a binary weakly invertible semi-input memory finite automaton C(Maf ) with delay 3, where the state graph of Ma is cyclic, the characterizations of the structures are given when its minimal 3-output weight is 1, 2, and 8, respectively. Because C(Maf ) is weakly invertible with delay 3 iff it is weakly inverse with delay 3, a partial characterization of the structure of binary feedforward inverses with delay 3 is obtained.

基金项目:Supported by the National Natural Science Foundation of China for Grand International Joint Project under Grant No.60310213 (国家自然科学基金重大国际(地区)合作研究项目); the National Natural Science Foundation for Distinguished Young Scholars of China under Grant No.60325206 (国家杰出青年科学基金) Supported by the National Natural Science Foundation of China for Grand International Joint Project under Grant No.60310213 (国家自然科学基金重大国际(地区)合作研究项目); the National Natural Science Foundation for Distinguished Young Scholars of China under Grant No.60325206 (国家杰出青年科学基金)